One of the main problems to be addressed when considering a networked control system is the large amount of bandwidth required by the different subsystems sharing the communication channel. Bandwidth and dynamic response of a plant are closely related. The faster the dynamics of the plant, the larger is its bandwidth. This usually translates into large frequency content on the controlling signal and a continuous exchange of information between the plant and the controller. In traditional control architectures, the feedback path makes the sensor information available to the controller continuously. In networked control systems, on the other hand, the sensor is connected to the actuator/controller by a network; that is, the feedback path is a network which typically has limited bandwidth and transfers information in a discrete time framework. These communication constraints make the task of designing a control system rather challenging.
Most of the approaches that have been proposed in the literature to overcome bandwidth constraints center around the idea of reducing the data transfer rate as much as possible to limit the bandwidth required from the network and free it for other tasks (e.g., other control loops using the network and/or non-control information exchange) without sacrificing stability and ultimately performance of the overall system (e.g., [1],[3]). This is typically accomplished by characterizing the maximum transfer time between information exchanges from the sensor to the controller/actuator, or, equivalently, the minimum frequency at which the sensor will send information to the actuator. Most results along these lines, however, have focused primarily on unconstrained linear plants where the transmission rate can be defined on the infinite time interval and consequently transfer times can be made arbitrarily long. In the presence of control constraints, however, this is not possible since constraints impose fundamental limitations on the set of initial conditions starting from where closed-loop stability can be guaranteed. For constrained processes, prolonged transfer periods can drive the state outside the stability region leading to instability. In addition to control constraints, nonlinear behavior and model uncertainty are two major issues that arise frequently in process control systems and must be accounted for explicitly in the control system design.
In this contribution, we present a networked control system architecture for nonlinear processes with model uncertainty and control constraints. We consider the case where the controller and the actuator are combined together into a single node, that is, the network is between the sensor and the controller/actuator node. Our objective is to reduce the network usage by allowing the sensor to transmit data at the lowest possible frequency that is needed for the stabilization of the plant under uncertainty and constraints. To this end, we initially use Lyapunov techniques to design a stabilizing bounded robust nonlinear control law and obtain an explicit characterization of its stability region in terms of the size of the uncertainty and the constraints. A plant model that approximates the actual plant behavior is then incorporated at the controller/actuator side, and used to implement the robust control law for the times between sensor transmissions. The use of a model to recreate the plant behavior allows the sensor to delay sending data since the model can provide an approximation of the plant dynamics. Feedback is then achieved by updating the model's state using the actual state of the plant that is provided by the sensor at each transmission instance. The fact that the update resets the error between the model and the plant states to zero at each transmission time allows modeling the overall networked control system as a nonlinear jump system and deriving sufficient conditions for stability in terms of the update time, the parameters of the plant and of its model. It is shown that, unlike the case of unconstrained systems, the maximum tolerable transfer time between sensors and actuators is critically dependent on the stability region -- which is a function of the uncertainty and constraints -- and cannot be chosen to be arbitrarily long even in the absence of model inaccuracies. The theoretical results are illustrated using a simulated model of an unstable plant comprised of multiple interconnected units, with actuators and sensors connected through a communication network.
References:
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